In general the relationship between DP and mutual information privacy constraints is not straightforward, although characterisations have been made in several settings [1]}, [2]}, [3]}. To our knowledge, a standard definition of DP privacy in the general RL setting is not agreed upon. Comparing to the DP constraint in the bandit setting, a key difference is that our constraint penalizes predictability of \(u_t\)  given \(a_t\) , in expectation over the distribution of \(u_t, a_t\) , while a DP constraint penalizes predictability between neighbouring trajectories, with no notion of the relative likelihood of these trajectories. This is a particularly important difference in the general RL setting, where the ability of a policy to change the distribution of states is a key feature.
